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Three conductors draw a current of 1 A, 2 A, and 3 A respectively, when connected in turn across a battery. If they are connected in series and the combination is connected across the same battery, the current drawn will be

Three conductors draw a current of 1 A, 2 A, and 3 A respectively, when connected in turn across a battery. If they are connected in series and the combination is connected across the same battery, the current drawn will be Correct Answer <span class="math-tex">\(\frac{6}{11}A\)</span>

CONCEPT:

  • Ohm's Law: A law stating that electric current is proportional to voltage and inversely proportional to resistance. Mathematically,

V = IR

where R is the resistance, I is current, and V is the voltage across the conductor.

  • Resistances in series combination: When two or more resistances are connected one after another such that the same current flows through them are called as resistances in series.

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The net resistance/equivalent resistance (R) of resistances in series is given by:

Equivalent resistance, R = R1 + R2

For parallel combination:

1/R = 1/R1 + 1/R2

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CALCULATION:

Given that conductors have current i1 = 1A; i2 = 2A; i3 = 3A;

Since conductors will have the same voltage in across/parallel connection. Let this voltage is 'V''

So R = V/I

R1 = V; R1 = V/2; R3 = V/3;

In series circuit

Req = R1 + R2 + R3;

Req = V + V/2 + V/3

Req = 11V/6

I = V/Req

I = 6/11 A

So the correct answer is option 3.

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